Question

iv) the scatter graph shows information about the cost of renting apartments and their distance from london. (a) describe the relationship shown in the scatter graph. (b) estimate the cost of renting an apartment 40km from london. (c) victor has £1100 to spend on rent. estimate how close he could live to london. (d) explain why it might not be sensible to use the scatter graph to estimate the price of rent for a property that is 250km from london.

Explanation:

Part (a)

To describe the relationship in a scatter graph, we analyze the trend of the points. Here, as the distance from London (x - axis) increases, the rent (y - axis) generally decreases. The points show a downward - sloping pattern, indicating a negative correlation. Also, the points are somewhat clustered around a general trend, so we can say there is a strong negative correlation between the distance from London and the cost of renting an apartment.

Step 1: Locate the x - value

We need to find the rent for an apartment 40 km from London. On the x - axis (distance from London), find the point corresponding to 40 km.

Step 2: Find the corresponding y - value

From the scatter graph, when we move up from 40 km on the x - axis until we reach the trend of the points (or the approximate position of the points), we can see that the corresponding rent (y - value) is around £900 (this is an estimate, and values around £800 - £1000 could be reasonable depending on how we interpret the trend, but looking at the graph, at 40 km, the point is near £800? Wait, no, let's re - examine. Wait, the x - axis is distance from London (km), y - axis is rent (£). At x = 40, looking at the graph, the point is at around £800? Wait, no, the grid: let's check the points. Wait, the last point is at x = 45, y = £800. At x = 40, maybe around £900? Wait, maybe I made a mistake. Wait, the x - axis: 0,5,10,15,20,25,30,35,40,45,50. The y - axis: 0,200,400,600,800,1000,1200,1400,1600,1800,2000. Let's see the trend. The points are decreasing. At x = 35, there is a point at £1200? No, wait, at x = 35, the y - value is around £1200? Wait, no, the point at x = 30 is £1000, x = 35 is £1200? No, that can't be. Wait, no, the y - axis is rent, so as x (distance) increases, y (rent) decreases. So at x = 5, y = 1600; x = 10, y = 1400; x = 15, y = 1400; x = 20, y = 1300; x = 25, y = 1200; x = 30, y = 1000; x = 35, y = 1200? No, that's an outlier? Wait, maybe the point at x = 35 is a mistake, or maybe I misread. Wait, the problem is to estimate. So for x = 40, we look at the trend. The point at x = 45 is at y = 800. So at x = 40, which is 5 km less than 45, we can estimate. If we assume a linear trend (even though it's a scatter graph), from x = 35 to x = 45, the rent decreases from, say, if at x = 35, maybe around £1000? No, this is confusing. Wait, the correct way is to look at the graph: when distance is 40 km, the corresponding rent (from the scatter plot) is approximately £900 (or maybe £800 - £1000). But looking at the graph, the point at x = 45 is at £800, so at x = 40, it's a bit higher, maybe £900.

Step 1: Locate the y - value

Victor has £1100 to spend on rent. So we look at the y - axis (rent) and find the point corresponding to £1100.

Step 2: Find the corresponding x - value

From the scatter graph, when we move horizontally from £1100 on the y - axis until we reach the trend of the points, we can see that the corresponding distance from London (x - value) is around 32 km (this is an estimate, values around 30 - 35 km could be reasonable. Let's see: at y = 1200, x = 25; at y = 1000, x = 30. So for y = 1100, which is between 1000 and 1200, the x - value should be between 25 and 30? Wait, no, wait: as y (rent) increases, x (distance) decreases. So if y = 1100, which is more than 1000 (y = 1000 at x = 30), so x should be less than 30. Wait, at y = 1200, x = 25. So the difference between y = 1200 (x = 25) and y = 1000 (x = 30) is 200 in y and 5 in x. So for a decrease of 200 in y, x increases by 5. So for a decrease of 100 in y (from 1200 to 1100), x increases by 2.5. So x = 25+2.5 = 27.5 km. So approximately 28 km. But from the graph, maybe around 30 km? Wait, the point at y = 1000 is at x = 30, y = 1200 at x = 25. So for y = 1100, x is around 27 - 28 km. But maybe the answer is around 30 km (depending on the graph's scale).

Answer:

There is a strong negative correlation between the distance from London and the cost of renting an apartment. As the distance from London increases, the rent of the apartment generally decreases.

Part (b)